# The molar mass of carbon dioxide is 0.045kg/mol. Calculate the density of the gas when the temperature is 273K and the pressure is 120000Pa..?

Dec 23, 2017

${\rho}_{\text{carbon dioxide}} = 2.4 \cdot g \cdot {L}^{-} 1$

#### Explanation:

We assume ideality, and we know that $P V = n R T$

And so $\frac{P}{R T} = \frac{n}{V} = \frac{\text{mass"/"molar mass}}{V}$

And so P/(RT)xx"molar mass"=underbrace("mass"/V)_("density", rho)...

And so we plug in the numbers....

rho_"carbon dioxide"=(120*kPa)/((273*Kxx8.31*L* kPa)/(K*mol))xx0.045*kg*mol^-1=2.38xx10^-3*kg*L^-1

Dec 23, 2017

The density is ${\text{2.3 kg/m}}^{3}$.

#### Explanation:

The molar mass of ${\text{CO}}_{2}$ is 0.044 kg/mol.

We can use the Ideal Gas Law to determine its density.

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Since $n = \frac{m}{M}$, we can substitute this to get

$p V = \left(\frac{m}{M}\right) R T$

We can rearrange this to

$p M = \frac{m}{V} R T$

But $\text{density"= "mass"/"volume}$ or color(brown)(bar(ul(|color(white)(a/a)ρ = m/Vcolor(white)(a/a)|)))" "

pM = ρRT

and

color(brown)(bar(ul(|color(white)(a/a)ρ = (pM)/(RT)color(white)(a/a)|)))" "

$p = \text{120 000 Pa}$
$M = \text{0.040 g/mol}$
$R = \text{8.314 Pa·m"^3·"K"^"-1""mol"^"-1}$
$T = \text{273K}$
ρ = ("120 000" color(red)(cancel(color(black)("Pa"))) × 0.044 color(white)(l) "kg"·color(red)(cancel(color(black)("mol"^"-1"))))/(8.314 color(red)(cancel(color(black)("Pa")))·"m"^3color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273color(red)(cancel(color(black)("K")))) = "2.3 kg/m"^3